Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting...

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Singly ionized (one electron removed) atoms are accelerated andthen passed through a velocity selector consisting of perpendicularelectric and magnetic fields. The electric field is 160 V/m and themagnetic field is 3.18Ã—10^?2 T . The ions next enter auniform magnetic field of magnitude 1.73Ã—10^?2 T that isoriented perpendicular to their velocity.
(A) If the radius of the path of the ions in the second magneticfield is 17.1 cm , what is their mass?

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4.5 Ratings (978 Votes)

Given E = 160 V/m

Â Â Â Â Â Â Â Â Â B =3.18Ã—10^?2Â Â Â Â T

Now the velocity of the ion when it emerges from the velocity selector is

Â Â Â Â Â Â Â Â Â Â Â Â Â Â v = E / B................(1)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (160 V/m) / (3.18Ã—10^?2Â Â Â Â T)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 5031.44 m/s

(a)

magnetic field B =1.75Ã—10^?2 T

radius of the path of the ions r = 17.5 cm = 0.175 m

magnetic force F = BvqÂ Â ................... (1)

from Newton's second law of motion ,

Â Â Â Â Â force F = maÂ Â

here , centripetal acceleration a = v²/r

Â Â Â Â Â Â force F = mv²/rÂ Â ................ (2)Â Â

compare eq (1) & eq (2) , we get

Â Â Â Â Â Â Â Â Bvq = mv²/rÂ Â

Â Â Â Â Â Â Â Â Bq = mv/rÂ Â

mass m = Bqr/v

Â Â Â Â Â Â Â Â Â Â Â Â = (1.75Ã—10^?2 T)(1.6*10^-19 C)(0.175 m) /(5031.44 m/s)

Â Â Â Â Â Â Â Â Â Â Â Â Â = 9.738*10^-26 kg

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Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting...

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